%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV763_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:19:27 PM UTC 2026
% Result : Theorem 3.06s 1.07s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 111 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 118 ( 56 ~; 47 |; 6 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 20 con; 0-4 aty)
% Number of variables : 23 ( 0 sgn 21 !; 2 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
event: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
agent: $tType ).
tff(type_def_9,type,
msg: $tType ).
tff(type_def_10,type,
nat: $tType ).
tff(type_def_11,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
bad: fun(agent,bool) ).
tff(func_def_1,type,
notes: ( agent * msg ) > event ).
tff(func_def_2,type,
says: ( agent * agent * msg ) > event ).
tff(func_def_3,type,
knows: ( agent * list(event) ) > fun(msg,bool) ).
tff(func_def_4,type,
used: list(event) > fun(msg,bool) ).
tff(func_def_5,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_7,type,
server: agent ).
tff(func_def_8,type,
spy: agent ).
tff(func_def_9,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_10,type,
keysFor: fun(msg,bool) > fun(nat,bool) ).
tff(func_def_11,type,
agent1: agent > msg ).
tff(func_def_12,type,
crypt: ( nat * msg ) > msg ).
tff(func_def_13,type,
key: nat > msg ).
tff(func_def_14,type,
mPair: ( msg * msg ) > msg ).
tff(func_def_15,type,
nonce: nat > msg ).
tff(func_def_16,type,
parts: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_17,type,
symKeys: fun(nat,bool) ).
tff(func_def_18,type,
nS_Sha254967238shared: fun(list(event),bool) ).
tff(func_def_19,type,
shrK: agent > nat ).
tff(func_def_20,type,
aa1:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
a: agent ).
tff(func_def_24,type,
a1: agent ).
tff(func_def_25,type,
aa: agent ).
tff(func_def_26,type,
b: agent ).
tff(func_def_27,type,
ba: agent ).
tff(func_def_28,type,
k: nat ).
tff(func_def_29,type,
kab: nat ).
tff(func_def_30,type,
na: msg ).
tff(func_def_31,type,
nAa: nat ).
tff(func_def_32,type,
nb: nat ).
tff(func_def_33,type,
x: msg ).
tff(func_def_34,type,
evs2: list(event) ).
tff(func_def_35,type,
sK0: ( list(event) * agent * nat * agent ) > msg ).
tff(func_def_36,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_37,type,
sK2: agent ).
tff(pred_def_1,type,
nS_Sha993195050haredp: list(event) > $o ).
tff(pred_def_2,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_3,type,
pp: bool > $o ).
tff(pred_def_4,type,
sQ3_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f79,axiom,
! [X0: list(event),X1: nat] :
( ~ member(msg,key(X1),used(X0))
=> ( member(nat,X1,symKeys)
=> ( member(list(event),X0,nS_Sha254967238shared)
=> ~ member(nat,X1,keysFor(parts(knows(spy,X0)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_new__keys__not__used) ).
tff(f84,axiom,
! [X0: fun(msg,bool),X1: msg,X2: nat] :
( member(msg,crypt(X2,X1),X0)
=> ( member(nat,X2,symKeys)
=> member(nat,X2,keysFor(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Crypt__imp__keysFor) ).
tff(f103,axiom,
member(list(event),evs2,nS_Sha254967238shared),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f104,axiom,
~ member(msg,key(kab),used(evs2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f105,axiom,
member(nat,kab,symKeys),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f109,conjecture,
( ( a != aa )
| ( na != nonce(nAa) )
| ( b != ba )
| ( k != kab )
| ( x != crypt(shrK(ba),mPair(key(kab),agent1(aa))) )
| ~ member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2)))
| ? [X0: agent] : member(event,says(X0,ba,crypt(shrK(ba),mPair(key(kab),agent1(aa)))),set(event,evs2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
tff(f110,negated_conjecture,
~ ( ( a != aa )
| ( na != nonce(nAa) )
| ( b != ba )
| ( k != kab )
| ( x != crypt(shrK(ba),mPair(key(kab),agent1(aa))) )
| ~ member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2)))
| ? [X0: agent] : member(event,says(X0,ba,crypt(shrK(ba),mPair(key(kab),agent1(aa)))),set(event,evs2)) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
tff(f162,plain,
! [X0: list(event),X1: nat] :
( ~ member(nat,X1,keysFor(parts(knows(spy,X0))))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(nat,X1,symKeys)
| member(msg,key(X1),used(X0)) ),
inference(ennf_transformation,[],[f79]) ).
tff(f163,plain,
! [X0: list(event),X1: nat] :
( ~ member(nat,X1,keysFor(parts(knows(spy,X0))))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(nat,X1,symKeys)
| member(msg,key(X1),used(X0)) ),
inference(flattening,[],[f162]) ).
tff(f166,plain,
! [X0: fun(msg,bool),X1: msg,X2: nat] :
( member(nat,X2,keysFor(X0))
| ~ member(nat,X2,symKeys)
| ~ member(msg,crypt(X2,X1),X0) ),
inference(ennf_transformation,[],[f84]) ).
tff(f167,plain,
! [X0: fun(msg,bool),X1: msg,X2: nat] :
( member(nat,X2,keysFor(X0))
| ~ member(nat,X2,symKeys)
| ~ member(msg,crypt(X2,X1),X0) ),
inference(flattening,[],[f166]) ).
tff(f191,plain,
( ( aa = a )
& ( nonce(nAa) = na )
& ( ba = b )
& ( kab = k )
& ( x = crypt(shrK(ba),mPair(key(kab),agent1(aa))) )
& member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2)))
& ! [X0: agent] : ~ member(event,says(X0,ba,crypt(shrK(ba),mPair(key(kab),agent1(aa)))),set(event,evs2)) ),
inference(ennf_transformation,[],[f110]) ).
tff(f319,plain,
! [X0: list(event),X1: nat] :
( ~ member(nat,X1,keysFor(parts(knows(spy,X0))))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(nat,X1,symKeys)
| member(msg,key(X1),used(X0)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f325,plain,
! [X2: nat,X0: fun(msg,bool),X1: msg] :
( ~ member(msg,crypt(X2,X1),X0)
| ~ member(nat,X2,symKeys)
| member(nat,X2,keysFor(X0)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f348,plain,
member(list(event),evs2,nS_Sha254967238shared),
inference(cnf_transformation,[],[f103]) ).
tff(f349,plain,
~ member(msg,key(kab),used(evs2)),
inference(cnf_transformation,[],[f104]) ).
tff(f350,plain,
member(nat,kab,symKeys),
inference(cnf_transformation,[],[f105]) ).
tff(f355,plain,
member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2))),
inference(cnf_transformation,[],[f191]) ).
tff(f357,plain,
kab = k,
inference(cnf_transformation,[],[f191]) ).
tff(f361,plain,
~ member(msg,key(k),used(evs2)),
inference(definition_unfolding,[],[f349,f357]) ).
tff(f362,plain,
member(nat,k,symKeys),
inference(definition_unfolding,[],[f350,f357]) ).
tff(f365,plain,
member(msg,crypt(k,nonce(nb)),parts(knows(spy,evs2))),
inference(definition_unfolding,[],[f355,f357]) ).
tff(f569,plain,
( ~ member(nat,k,symKeys)
| member(nat,k,keysFor(parts(knows(spy,evs2)))) ),
inference(resolution,[],[f325,f365]) ).
tff(f578,definition,
( spl4_5
<=> member(nat,k,symKeys) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f579,plain,
( ~ member(nat,k,symKeys)
| spl4_5 ),
inference(avatar_component_clause,[],[f578]) ).
tff(f582,definition,
( spl4_6
<=> member(nat,k,keysFor(parts(knows(spy,evs2)))) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
tff(f583,plain,
( member(nat,k,keysFor(parts(knows(spy,evs2))))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f582]) ).
tff(f584,plain,
( spl4_6
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f569,f578,f582]) ).
tff(f585,plain,
( $false
| spl4_5 ),
inference(resolution,[],[f579,f362]) ).
tff(f586,plain,
spl4_5,
inference(avatar_contradiction_clause,[],[f585]) ).
tff(f629,plain,
( ~ member(list(event),evs2,nS_Sha254967238shared)
| ~ member(nat,k,symKeys)
| member(msg,key(k),used(evs2))
| ~ spl4_6 ),
inference(resolution,[],[f319,f583]) ).
tff(f631,definition,
( spl4_7
<=> member(msg,key(k),used(evs2)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
tff(f632,plain,
( member(msg,key(k),used(evs2))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f631]) ).
tff(f634,definition,
( spl4_8
<=> member(list(event),evs2,nS_Sha254967238shared) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
tff(f635,plain,
( ~ member(list(event),evs2,nS_Sha254967238shared)
| spl4_8 ),
inference(avatar_component_clause,[],[f634]) ).
tff(f636,plain,
( spl4_7
| ~ spl4_5
| ~ spl4_8
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f629,f582,f634,f578,f631]) ).
tff(f637,plain,
( $false
| spl4_8 ),
inference(resolution,[],[f635,f348]) ).
tff(f638,plain,
spl4_8,
inference(avatar_contradiction_clause,[],[f637]) ).
tff(f639,plain,
( $false
| ~ spl4_7 ),
inference(resolution,[],[f632,f361]) ).
tff(f640,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f639]) ).
cnf(s3,plain,
( ~ spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f584]) ).
cnf(s4,plain,
spl4_5,
inference(sat_conversion,[],[f586]) ).
cnf(s5,plain,
( ~ spl4_5
| ~ spl4_6
| spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f636]) ).
cnf(s6,plain,
spl4_8,
inference(sat_conversion,[],[f638]) ).
cnf(s7,plain,
~ spl4_7,
inference(sat_conversion,[],[f640]) ).
cnf(s8,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(rat,[],[s5,s6,s7]) ).
cnf(s9,plain,
~ spl4_6,
inference(rat,[],[s8,s4]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s9,s4]) ).
tff(f641,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV763_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 12:32:52 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.06/1.07 % (322626)Detected formulas, will run a generic FOF schedule.
% 3.06/1.07 % (322631)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=496450932:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.06/1.07 % (322637)dis-21_1_sil=8000:lcm=predicate:random_seed=1265531862:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.06/1.07 % (322634)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1674142980:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.06/1.07 % (322635)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2123083184:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.06/1.07 % (322632)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2384228631:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.06/1.07 % (322633)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3877769476:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.06/1.07 % (322636)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1933123395:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.06/1.07 % (322634)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.06/1.07 % (322633)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.06/1.07 % (322634)Refutation not found, incomplete strategy
% 3.06/1.07 % (322634)------------------------------
% 3.06/1.07 % (322634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.07 % (322634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.07 % (322634)CaDiCaL version: 2.1.3
% 3.06/1.07 % (322634)Termination reason: Refutation not found, incomplete strategy
% 3.06/1.07 % (322634)Time elapsed: 0.007 s
% 3.06/1.07 % (322634)Peak memory usage: 88 MB
% 3.06/1.07 % (322634)Instructions burned: 12 (million)
% 3.06/1.07 % (322637)First to succeed.
% 3.06/1.07 % (322637)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-322626"
% 3.06/1.07 % (322636)Also succeeded, but the first one will report.
% 3.06/1.07 % (322635)Instruction limit reached!
% 3.06/1.07 % (322635)------------------------------
% 3.06/1.07 % (322635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.07 % (322635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.07 % (322635)CaDiCaL version: 2.1.3
% 3.06/1.07 % (322635)Termination reason: Instruction limit
% 3.06/1.07 % (322635)Termination phase: Saturation
% 3.06/1.07 % (322635)Time elapsed: 0.064 s
% 3.06/1.07 % (322635)Peak memory usage: 88 MB
% 3.06/1.07 % (322635)Instructions burned: 120 (million)
% 3.06/1.07 % Exception at run slice level
% 3.06/1.07 User error: GNN currently only supports monomorphic FOL.
% 3.06/1.07 % (322645)lrs+10_1_sil=8000:sp=occurrence:random_seed=2021438996:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.06/1.07 % (322634)------------------------------
% 3.06/1.07 % (322634)------------------------------
% 3.06/1.07 % (322637)Refutation found. Thanks to Tanya!
% 3.06/1.07 % SZS status Theorem for theBenchmark
% 3.06/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.16 % (322637)------------------------------
% 3.46/1.16 % (322637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.16 % (322637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.16 % (322637)CaDiCaL version: 2.1.3
% 3.46/1.16 % (322637)Termination reason: Refutation
% 3.46/1.16 % (322637)Time elapsed: 0.011 s
% 3.46/1.16 % (322637)Peak memory usage: 89 MB
% 3.46/1.16 % (322637)Instructions burned: 17 (million)
% 3.46/1.16 % (322637)------------------------------
% 3.46/1.16 % (322637)------------------------------
% 3.46/1.16 % (322626)Success in time 0.42 s
% 3.46/1.16 % Vampire exiting
%------------------------------------------------------------------------------